Operando Li metal plating diagnostics via MHz band electromagnetics

A nondestructive detection method for internal Li-metal plating in lithium-ion batteries is essential to improve their lifetime. Here, we demonstrate a direct Li-metal detection technology that focuses on electromagnetic behaviour. Through an interdisciplinary approach combining the ionic behaviour of electrochemical reactions at the negative electrode and the electromagnetic behaviour of electrons based on Maxwell’s equations, we find that internal Li-metal plating can be detected by the decrease in real part of the impedance at high-frequency. This finding enables simpler diagnostics when compared to data-driven analysis because we can correlate a direct response from the electronic behaviour to the metallic material property rather changes in the ionic behaviour. We test this response using commercial Li-ion batteries subject to extremely fast charging conditions to induce Li-metal plating. From this, we develop a battery sensor that detects and monitors the cycle-by-cycle growth of Li-metal plating. This work not only contributes to advancing future Li-ion battery development but may also serve as a tool for Li-metal plating monitoring in real-field applications to increase the useable lifetime of Li-ion batteries and to prevent detrimental Li-metal plating.


Supplementary Discussion 1: High-frequency current distribution on the boundary between two different conductivity materials
A cylindrical (radius = R, height = Z) coordinate system is used to analyse the high-frequency current density characteristics at the boundary of different conductive materials.Equation 1 is derived from Ohm's law: if the current density  = (  ,   ,   ) , electric field strength  = (  ,   ,   ) and electrical conductivity σ(z) are functions that fluctuate only in the Z direction, ×  =  × (). (2) Equation 2 can be described as Eqs.(5) Current continuity ( •  = ) simplifies Eq. 5 to Eqs. 6 and 7: Finally, the behaviour of AC is described using Eq. 8 and  =   : Using Eq. 8, we estimate the current distribution on the σ interface.In the wide cylinder model, aspect R >> Z allows 1    ≈ 0, and symmetry allows   = 0.
If () is a constant independent of z, then Eq. 8 can be represented as follows: where The well-known skin effect (Eq. 11) can be derived from Eq. 10. (11) In the battery model, () in the layered materials is not constant and induces additional current distribution along the r axis.Based on the above equations, we observed a trend in   at each () boundary.In each region,   attempts to distribute according to Eq. 12.In the boundary zone,   flows and varies continuously at the same time.The current continuity ( •  = ) changes the relation between   and   : where   is set to 0. When each region has ( 1 ) =  1 and ( 2 ) =  2 , the approximated current   =   (, ) and   =   (, ) can be calculated in the neighborhood of the boundary where () denotes area-specific constant amplitudes.The total current in the z direction = ; hence, satisfy Eq. 15, The trend of the boundary current   can be derived by reformulating Eqs. 13 and 15, When  1 is the conductivity of the active material and  2 is the conductivity of the electrolytic solution, we can estimate the vertical current of the electrolytic solution layer as   ( 2 , ) =  =  with  2  ≪  1 .Then, Eq. 17 is simplified as follows: where ( 1 ) can be described by B in Eq. 15: Equation 18 summarizes the trend of the current distribution in the surface direction (r) on the higher conductivity surface of different conductivity materials.Moreover, this current is increased monotonically by  1 .Consequently, the Li-metal plating that increases the digits of  1 significantly changes the Hz of a battery.

Frequency
Verification of the ECM for EIS.a-c The ECM of electrolyte Zelec at high frequency.a A cell configuration for verifying the high-frequency response of the Zelec.The cell is designed as an electric double-layer capacitor that uses the same electrolyte and separator as the laminate cell shown in the Supplementary Fig. 3.The thickness of the electrolyte is changed by stacking the separator.b,c Frequency characteristics of the measured real part of the impedance Re[Z] and estimated equivalent circuit of Zelec.Relec represents the electrolyte resistance, and Celec represents the geometrical stray capacitance between the collector plates.The Relec is proportional to the thickness of the electrolyte up to 4 MHz.However, Re[Z] converges to the same value from 70 MHz with increasing value by the skin effect and the proximity effect.This behaviour can be modelled by the RC model shown in (c), which uses the conductivity and relative dielectric constant as σelec= 0.01 [S/m] and εelec = 81, respectively, which are used in other simulations, such as the Supplementary Fig. 2. The estimated RC model has a cut-off of approximately 10 MHz, and Re[Zelec] can converge to zero by increasing the frequency.In addition, Relec can be sufficiently small by increasing the cross-sectional area of Selec in a large-capacity battery.Therefore, the high-frequency measurement can deal with ionic degradation as negligible, and even Zelec might change its resistance by degradation.d,e Example of a low-frequency EIS result in the 18650-type battery ID [#Z] shown in Fig. 4, which has a Li-metal plate by degradation.d The Cole-Cole plot from 0.1Hz to 10 kHz.e Re[Z] vs. frequency.The resistance is broadly increased by Li-metal plating mixed with other degradation factors.Laminate cell modelling and visualization of high-frequency electromagnetic behaviour by computational analysis.a Overall negative-facing cell model in a high-frequency multiphysics simulation (COMSOL6.0).The cell size is referenced in the laminated pouch cell used in the experimental result shown in the Supplementary Fig. 3. b Mesh design.A squared mesh was manipulated as the gradationed size in the edges for monitoring the high-frequency current concentration.c Design of the lamination slices and parameters.The graphite layer was sliced into 10 layers, and special conductivity can be applied to the top two graphite layers to emulate Li-metal plating.d Simulation result of the overall current flow at 10 MHz without Li-metal plating.The current spread in the top and bottom collector layers and down straight in the other layers.e Simulation result of the overall current flow at 10 MHz with the Li-metal layer.There is an additional surface current in the middle of the battery, where the conductivity changes from that of graphite to that of Li metal.f,g,h Overall simulation results.∆Z is calculated by the difference between (d) and (e).
Experimental verification of the negative correlation between Li metal and highfrequency impedance (analytical inspection).a Photographs of the laminate-type pouch cell.The cells were connected to the PCB with SMA connectors.b Table summarising the results of the degradation tests conducted on the laminate-type pouch cells, including images of the anode, degradation conditions and capacity loss of the Li-deposited cells.[I] Initial state of the battery used as a reference.Li metal is deposited in [II][IV][V] batteries via cycle tests.Following a cycle test, [III] is exposed to a storage test at a high temperature.At high temperatures, some of the precipitated Li metal transformed into SEI, resulting in the formation of dark brown precipitates.c Conventional ECM valid for low-frequency 10 .d Proposed ECM applicable to the high-frequency region.The presence of high-frequency impedance Zhf, shown as impedance behaviour in the MHz band, including Li-metal plating, deviates from the conventional ECM. e Cole-Cole plot of the measured impedance curves (Zmes) and fitting curves (Zmodel) by the conventional ECM.These curves were fitted in the range of 100 mHz to 750 kHz and showed good agreement with the measured values at low frequencies, regardless of the degradation condition.f Comparison of the measured and fitted values of the real component of the impedance at high frequency.The measured and fitted values were consistent up to 1 MHz but from 2MHz to 3 MHz.The measured values started to increase, whereas the fitted values monotonically decreased.This difference corresponded to Zhf. g Relationship between the Li metal and Re[Zmes − Zmodel].The negative correlation between the volume of the Li metal and Re[Zmes − Zmodel] can be confirmed.In the electromagnetic simulation, the distinction between [I] and [II]-[V] is equivalent to the Re[ΔZ] in Fig. 3.
Inductance R 0 : Geometry and Solution Resistance R 1-3 : Carrier Transfer Resistance Q 1-3 : Constant Phase Element Z hf : High-frequency electrode impedance that is described Fig.1b

Supplementary Fig. 4 |
Overall high-frequency measurement result of the 18650-type battery used in Fig. 4 (1500 mAh, LFP). a Frequency vs. impedance from 0.1MHz to 100 MHz.Impedance |Z| and Re[Z] are proportional to the frequency.Compared to the laminated pouch cell shown in Supplementary Fig.3, an 18650-type battery behaves as an inductor in this frequency range.In the 10 MHz frequency band, both the real and imaginary components have a convex profile.This local behaviour suggests a second potential for this high-frequency diagnosis that directly monitors the status of health (SOH), as summarised in the Supplementary Fig.5.b ∆Z vs. frequency with dependency against the state of charge (SOC).Re[∆Z] is stable against the SOC status in the MHz range used for Li-metal detection.This feature is important for field use since it does not require battery conditioning equipment such as precise charger systems for SOC adjustment.

Fig. 5 |
Further experimental results for 18650-type batteries.a-d Geometrical features and initial characteristics of the evaluated 18650-type batteries.Battery (a) is LFP/1500 mAh with Re[Z1MHz] = 300 mΩ as the initial value.Battery (b) is NCA/3350 mAh that has Re[Z1MHz] = 290 mΩ as the initial value.Battery (c) is NCM/2500 mAh and has Re[Z1MHz] = 780 mΩ as the initial value.Battery cells (a) and (b) have the cathode terminal in the center of the aluminium collector.The battery cell (c) has the cathode terminal on the edge of the aluminium collector.Only battery cell (b) has an anode collector (copper) in the outer surface, whereas the others have dielectric films between its housing.In the battery shown in (c), only excessive rapid charge degradation results are measured due to a lack of sample cells.e-g Measured impedance change at 1MHz.The results show that our method is not affected by the material but is affected by the structural features.e,h The results of the LFP-type (Repost of Fig.4) and the NCM-type.Since battery (c) has the longest terminal-to-terminal edge, the negative collation between SOH and Re[∆Z1MHz] in (f) can be observed to stronger than that in other batteries.f The result of the NCA-type is scattered compared to the LFP-type (d) or NCM-type (f).The reason for this scattering is assumed to be geometrical noise.The unstable outer contact clearly affects the high-frequency impedance by interfering with the anode collector's current flow.h-j Measured impedance change at 20 MHz in each battery.In contrast to the 1 MHz results, both blue and red dots are blended and aligned along the proportionate lines against the SOH.Although a scientific review is needed, it might be applied as a technique for rapid capacity estimation.